Graph forms
for C4 [ 220, 7 ] = PS(20,11;3)
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On this page are computer-accessible forms for the graph C4[ 220, 7 ] =
PS(20,11;3).
(I) Following is a form readable by MAGMA:
g:=Graph<220|{ {66, 67}, {176, 177}, {32, 34}, {197, 199}, {88, 90}, {33, 35},
{20, 23}, {76, 79}, {121, 122}, {132, 135}, {107, 111}, {162, 166}, {163, 167},
{40, 45}, {208, 213}, {187, 190}, {185, 188}, {98, 103}, {96, 101}, {75, 78},
{42, 47}, {131, 134}, {152, 157}, {154, 159}, {40, 46}, {209, 215}, {208, 214},
{97, 103}, {96, 102}, {41, 47}, {152, 158}, {153, 159}, {11, 12}, {209, 214},
{186, 189}, {104, 111}, {97, 102}, {41, 46}, {130, 133}, {153, 158}, {160, 167},
{16, 24}, {71, 79}, {70, 78}, {17, 25}, {18, 26}, {19, 27}, {20, 28}, {21, 29},
{22, 30}, {128, 136}, {129, 137}, {130, 138}, {131, 139}, {132, 140}, {180,
188}, {181, 189}, {182, 190}, {183, 191}, {32, 41}, {198, 207}, {196, 205},
{194, 203}, {192, 201}, {86, 95}, {84, 93}, {82, 91}, {80, 89}, {49, 56}, {51,
58}, {53, 60}, {55, 62}, {161, 168}, {163, 170}, {165, 172}, {4, 14}, {99, 105},
{98, 104}, {5, 15}, {39, 45}, {64, 74}, {65, 75}, {112, 122}, {113, 123}, {116,
126}, {117, 127}, {150, 156}, {151, 157}, {176, 186}, {33, 42}, {197, 206},
{193, 202}, {99, 104}, {85, 94}, {81, 90}, {50, 57}, {54, 61}, {151, 156}, {162,
169}, {1, 13}, {2, 14}, {3, 15}, {52, 56}, {53, 57}, {54, 58}, {55, 59}, {64,
76}, {65, 77}, {112, 124}, {113, 125}, {114, 126}, {115, 127}, {164, 168}, {165,
169}, {21, 24}, {194, 207}, {192, 205}, {82, 95}, {80, 93}, {150, 155}, {2, 12},
{198, 200}, {87, 89}, {3, 13}, {16, 30}, {17, 31}, {66, 76}, {114, 124}, {115,
125}, {128, 142}, {129, 143}, {149, 155}, {177, 191}, {22, 25}, {195, 204},
{193, 206}, {83, 92}, {81, 94}, {48, 63}, {52, 59}, {160, 175}, {164, 171}, {34,
50}, {204, 220}, {203, 219}, {202, 218}, {201, 217}, {200, 216}, {199, 215},
{35, 51}, {36, 52}, {37, 53}, {38, 54}, {39, 55}, {34, 51}, {202, 219}, {200,
217}, {105, 120}, {103, 118}, {101, 116}, {36, 53}, {38, 55}, {45, 60}, {47,
62}, {161, 176}, {14, 28}, {101, 119}, {100, 118}, {74, 88}, {71, 85}, {70, 84},
{15, 29}, {45, 63}, {67, 81}, {12, 31}, {201, 218}, {195, 208}, {106, 121},
{102, 117}, {79, 92}, {68, 87}, {37, 54}, {46, 61}, {135, 148}, {139, 152}, {4,
16}, {5, 17}, {6, 18}, {7, 19}, {111, 123}, {166, 178}, {167, 179}, {172, 184},
{173, 185}, {174, 186}, {175, 187}, {67, 86}, {196, 209}, {78, 91}, {134, 147},
{140, 153}, {6, 16}, {69, 83}, {7, 17}, {12, 26}, {13, 27}, {68, 82}, {167,
177}, {174, 184}, {175, 185}, {1, 22}, {203, 220}, {100, 115}, {35, 52}, {133,
146}, {135, 144}, {141, 154}, {143, 152}, {15, 23}, {77, 85}, {76, 84}, {75,
83}, {74, 82}, {73, 81}, {72, 80}, {105, 112}, {109, 116}, {107, 114}, {136,
145}, {138, 147}, {140, 149}, {142, 151}, {8, 18}, {207, 213}, {206, 212}, {9,
19}, {42, 48}, {43, 49}, {168, 178}, {169, 179}, {172, 182}, {173, 183}, {43,
48}, {207, 212}, {106, 113}, {110, 117}, {137, 146}, {141, 150}, {8, 20}, {110,
114}, {109, 113}, {108, 112}, {9, 21}, {10, 22}, {133, 153}, {134, 154}, {168,
180}, {169, 181}, {170, 182}, {171, 183}, {44, 49}, {206, 211}, {77, 80}, {69,
88}, {136, 149}, {138, 151}, {166, 187}, {10, 20}, {205, 211}, {204, 210}, {103,
121}, {102, 120}, {73, 87}, {72, 86}, {11, 21}, {44, 50}, {142, 144}, {143,
145}, {170, 180}, {171, 181}, {104, 119}, {205, 210}, {199, 216}, {108, 115},
{137, 150}, {139, 148}, {78, 98}, {79, 99}, {13, 32}, {158, 176}, {14, 33}, {89,
105}, {94, 110}, {93, 109}, {92, 108}, {91, 107}, {90, 106}, {144, 160}, {145,
161}, {146, 162}, {147, 163}, {148, 164}, {149, 165}, {90, 107}, {92, 109},
{144, 161}, {146, 163}, {148, 165}, {155, 170}, {157, 172}, {159, 174}, {18,
32}, {19, 33}, {156, 174}, {157, 175}, {23, 36}, {93, 110}, {89, 106}, {83, 96},
{27, 40}, {31, 44}, {145, 162}, {158, 173}, {24, 44}, {28, 41}, {86, 99}, {84,
97}, {30, 43}, {155, 173}, {29, 42}, {91, 108}, {87, 96}, {85, 98}, {31, 40},
{147, 164}, {156, 171}, {26, 35}, {88, 97}, {28, 37}, {30, 39}, {159, 166}, {94,
100}, {95, 101}, {154, 160}, {25, 34}, {95, 100}, {29, 38}, {23, 43}, {24, 37},
{26, 39}, {25, 38}, {27, 36}, {188, 208}, {189, 209}, {46, 64}, {47, 65}, {49,
64}, {51, 66}, {48, 66}, {183, 197}, {178, 192}, {179, 193}, {182, 196}, {50,
65}, {191, 204}, {60, 72}, {61, 73}, {62, 74}, {63, 75}, {56, 77}, {190, 203},
{188, 201}, {177, 196}, {179, 198}, {62, 72}, {63, 73}, {180, 194}, {181, 195},
{178, 197}, {191, 200}, {189, 202}, {184, 192}, {187, 195}, {186, 194}, {185,
193}, {190, 199}, {57, 67}, {60, 70}, {61, 71}, {56, 68}, {57, 69}, {58, 70},
{59, 71}, {58, 68}, {184, 198}, {59, 69}, {7, 212}, {11, 216}, {2, 215}, {6,
211}, {1, 214}, {5, 210}, {1, 217}, {2, 218}, {3, 219}, {4, 220}, {8, 210}, {9,
211}, {3, 216}, {7, 220}, {4, 217}, {6, 219}, {8, 213}, {10, 215}, {10, 212},
{11, 213}, {5, 218}, {9, 214}, {111, 132}, {122, 136}, {123, 137}, {126, 140},
{127, 141}, {124, 143}, {116, 128}, {117, 129}, {118, 130}, {119, 131}, {123,
142}, {118, 128}, {119, 129}, {124, 138}, {125, 139}, {122, 141}, {125, 133},
{126, 134}, {127, 135}, {120, 130}, {121, 131}, {120, 132} }>;
(II) A more general form is to represent the graph as the orbit of {66, 67}
under the group generated by the following permutations:
a: (1, 12, 23, 34, 45, 56, 67, 78, 89, 100, 111, 122, 133, 144, 155, 166, 177,
188, 199, 210)(2, 15, 32, 39, 49, 57, 70, 87, 94, 104, 112, 125, 142, 149, 159,
167, 180, 197, 204, 214)(3, 18, 30, 44, 53, 58, 73, 85, 99, 108, 113, 128, 140,
154, 163, 168, 183, 195, 209, 218)(4, 21, 28, 38, 46, 59, 76, 83, 93, 101, 114,
131, 138, 148, 156, 169, 186, 193, 203, 211)(5, 13, 26, 43, 50, 60, 68, 81, 98,
105, 115, 123, 136, 153, 160, 170, 178, 191, 208, 215)(6, 16, 24, 37, 54, 61,
71, 79, 92, 109, 116, 126, 134, 147, 164, 171, 181, 189, 202, 219)(7, 19, 33,
42, 47, 62, 74, 88, 97, 102, 117, 129, 143, 152, 157, 172, 184, 198, 207,
212)(8, 22, 31, 36, 51, 63, 77, 86, 91, 106, 118, 132, 141, 146, 161, 173, 187,
196, 201, 216)(9, 14, 29, 41, 55, 64, 69, 84, 96, 110, 119, 124, 139, 151, 165,
174, 179, 194, 206, 220)(10, 17, 27, 35, 48, 65, 72, 82, 90, 103, 120, 127, 137,
145, 158, 175, 182, 192, 200, 213)(11, 20, 25, 40, 52, 66, 75, 80, 95, 107, 121,
130, 135, 150, 162, 176, 185, 190, 205, 217) (III) Last is Groups&Graphs. Copy everything between (not including)
the lines of asterisks into a plain text file and save it as "graph.txt". Then
launch G&G (Groups&Graphs) and select Read Text from the File menu.
**************
&Graph **************
b: (2, 11)(3, 10)(4, 9)(5, 8)(6, 7)(13, 22)(14, 21)(15, 20)(16, 19)(17, 18)(24,
33)(25, 32)(26, 31)(27, 30)(28, 29)(35, 44)(36, 43)(37, 42)(38, 41)(39, 40)(46,
55)(47, 54)(48, 53)(49, 52)(50, 51)(57, 66)(58, 65)(59, 64)(60, 63)(61, 62)(68,
77)(69, 76)(70, 75)(71, 74)(72, 73)(79, 88)(80, 87)(81, 86)(82, 85)(83, 84)(90,
99)(91, 98)(92, 97)(93, 96)(94, 95)(101, 110)(102, 109)(103, 108)(104, 107)(105,
106)(112, 121)(113, 120)(114, 119)(115, 118)(116, 117)(123, 132)(124, 131)(125,
130)(126, 129)(127, 128)(134, 143)(135, 142)(136, 141)(137, 140)(138, 139)(145,
154)(146, 153)(147, 152)(148, 151)(149, 150)(156, 165)(157, 164)(158, 163)(159,
162)(160, 161)(167, 176)(168, 175)(169, 174)(170, 173)(171, 172)(178, 187)(179,
186)(180, 185)(181, 184)(182, 183)(189, 198)(190, 197)(191, 196)(192, 195)(193,
194)(200, 209)(201, 208)(202, 207)(203, 206)(204, 205)(211, 220)(212, 219)(213,
218)(214, 217)(215, 216)
c: (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11)(12, 13, 14, 15, 16, 17, 18, 19, 20, 21,
22)(23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33)(34, 35, 36, 37, 38, 39, 40, 41,
42, 43, 44)(45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55)(56, 57, 58, 59, 60, 61,
62, 63, 64, 65, 66)(67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77)(78, 79, 80, 81,
82, 83, 84, 85, 86, 87, 88)(89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99)(100,
101, 102, 103, 104, 105, 106, 107, 108, 109, 110)(111, 112, 113, 114, 115, 116,
117, 118, 119, 120, 121)(122, 123, 124, 125, 126, 127, 128, 129, 130, 131,
132)(133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143)(144, 145, 146, 147,
148, 149, 150, 151, 152, 153, 154)(155, 156, 157, 158, 159, 160, 161, 162, 163,
164, 165)(166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176)(177, 178, 179,
180, 181, 182, 183, 184, 185, 186, 187)(188, 189, 190, 191, 192, 193, 194, 195,
196, 197, 198)(199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209)(210, 211,
212, 213, 214, 215, 216, 217, 218, 219, 220)
C4[ 220, 7 ]
220
-1 22 13 214 217
-2 12 14 215 218
-3 13 15 216 219
-4 220 14 16 217
-5 210 15 17 218
-6 211 16 18 219
-7 220 212 17 19
-8 210 213 18 20
-9 211 214 19 21
-10 22 212 215 20
-11 12 213 216 21
-12 11 2 26 31
-13 1 3 27 32
-14 33 2 4 28
-15 23 3 5 29
-16 24 4 6 30
-17 25 5 7 31
-18 26 6 8 32
-19 33 27 7 9
-20 23 28 8 10
-21 11 24 29 9
-22 1 25 30 10
-23 36 15 20 43
-24 44 37 16 21
-25 22 34 38 17
-26 12 35 39 18
-27 13 36 40 19
-28 14 37 41 20
-29 15 38 42 21
-30 22 16 39 43
-31 44 12 17 40
-32 34 13 18 41
-33 35 14 19 42
-34 25 50 51 32
-35 33 26 51 52
-36 23 27 52 53
-37 24 28 53 54
-38 55 25 29 54
-39 55 45 26 30
-40 45 46 27 31
-41 46 47 28 32
-42 33 47 48 29
-43 23 48 49 30
-44 24 49 50 31
-45 60 39 40 63
-46 61 40 41 64
-47 62 41 42 65
-48 66 63 42 43
-49 44 56 64 43
-50 44 34 57 65
-51 66 34 35 58
-52 56 35 36 59
-53 57 36 37 60
-54 58 37 38 61
-55 59 38 39 62
-56 77 68 49 52
-57 67 69 50 53
-58 68 70 51 54
-59 55 69 71 52
-60 45 70 72 53
-61 46 71 73 54
-62 55 47 72 74
-63 45 48 73 75
-64 46 49 74 76
-65 77 47 50 75
-66 67 48 51 76
-67 66 57 81 86
-68 56 58 82 87
-69 88 57 59 83
-70 78 58 60 84
-71 79 59 61 85
-72 80 60 62 86
-73 81 61 63 87
-74 88 82 62 64
-75 78 83 63 65
-76 66 79 84 64
-77 56 80 85 65
-78 91 70 75 98
-79 99 92 71 76
-80 77 89 93 72
-81 67 90 94 73
-82 68 91 95 74
-83 69 92 96 75
-84 70 93 97 76
-85 77 71 94 98
-86 99 67 72 95
-87 89 68 73 96
-88 90 69 74 97
-89 80 105 106 87
-90 88 81 106 107
-91 78 82 107 108
-92 79 83 108 109
-93 110 80 84 109
-94 110 100 81 85
-95 100 101 82 86
-96 101 102 83 87
-97 88 102 103 84
-98 78 103 104 85
-99 79 104 105 86
-100 115 94 95 118
-101 116 95 96 119
-102 117 96 97 120
-103 121 118 97 98
-104 99 111 119 98
-105 99 89 112 120
-106 121 89 90 113
-107 111 90 91 114
-108 112 91 92 115
-109 113 92 93 116
-110 114 93 94 117
-111 132 123 104 107
-112 122 124 105 108
-113 123 125 106 109
-114 110 124 126 107
-115 100 125 127 108
-116 101 126 128 109
-117 110 102 127 129
-118 100 103 128 130
-119 101 104 129 131
-120 132 102 105 130
-121 122 103 106 131
-122 121 112 136 141
-123 111 113 137 142
-124 143 112 114 138
-125 133 113 115 139
-126 134 114 116 140
-127 135 115 117 141
-128 136 116 118 142
-129 143 137 117 119
-130 133 138 118 120
-131 121 134 139 119
-132 111 135 140 120
-133 146 125 130 153
-134 154 147 126 131
-135 132 144 148 127
-136 122 145 149 128
-137 123 146 150 129
-138 124 147 151 130
-139 125 148 152 131
-140 132 126 149 153
-141 154 122 127 150
-142 144 123 128 151
-143 145 124 129 152
-144 135 160 161 142
-145 143 136 161 162
-146 133 137 162 163
-147 134 138 163 164
-148 165 135 139 164
-149 165 155 136 140
-150 155 156 137 141
-151 156 157 138 142
-152 143 157 158 139
-153 133 158 159 140
-154 134 159 160 141
-155 170 149 150 173
-156 171 150 151 174
-157 172 151 152 175
-158 176 173 152 153
-159 154 166 174 153
-160 154 144 167 175
-161 176 144 145 168
-162 166 145 146 169
-163 167 146 147 170
-164 168 147 148 171
-165 169 148 149 172
-166 187 178 159 162
-167 177 179 160 163
-168 178 180 161 164
-169 165 179 181 162
-170 155 180 182 163
-171 156 181 183 164
-172 165 157 182 184
-173 155 158 183 185
-174 156 159 184 186
-175 187 157 160 185
-176 177 158 161 186
-177 176 167 191 196
-178 166 168 192 197
-179 198 167 169 193
-180 188 168 170 194
-181 189 169 171 195
-182 190 170 172 196
-183 191 171 173 197
-184 198 192 172 174
-185 188 193 173 175
-186 176 189 194 174
-187 166 190 195 175
-188 201 180 185 208
-189 209 202 181 186
-190 187 199 203 182
-191 177 200 204 183
-192 178 201 205 184
-193 179 202 206 185
-194 180 203 207 186
-195 187 181 204 208
-196 209 177 182 205
-197 199 178 183 206
-198 200 179 184 207
-199 190 215 216 197
-200 198 191 216 217
-201 188 192 217 218
-202 189 193 218 219
-203 220 190 194 219
-204 220 210 191 195
-205 210 211 192 196
-206 211 212 193 197
-207 198 212 213 194
-208 188 213 214 195
-209 189 214 215 196
-210 5 204 205 8
-211 6 205 206 9
-212 7 206 207 10
-213 11 8 207 208
-214 209 1 9 208
-215 209 199 2 10
-216 11 199 200 3
-217 1 200 201 4
-218 2 201 202 5
-219 3 202 203 6
-220 4 203 204 7
0